While Delhi gets a good deal colder than Bombay ever does, it isn't as cold as the UK. It is considered part of "the plains". You'd probably find a flowering cycle closer to what you're familiar with in the hills and mountains further north.
(A sidelight here: if you ever travel back to India again, I'd recommend a visit to the Valley of Flowers. You'd have to fly out from Delhi (or take a train) to Haridwar, and then, via road - busses or hired cars available - for another whole day, but from what people tell me, it's worth the effort. Summer would be the best time.)
Many of the flowers in the plains are descendants of plants brought in over the centuries by those great garden lovers, the Mughals, and later, by Englishmen wanting to make a foreign strand forever a little more English. So the flowers you saw may have just been distant cousins of those your own garden. Much like you probably have relatives in India you may never have heard of. I have some kin in the UK. (My direct paternal line is Irish, I'm told, so maybe some fiery ancestor is turning in his grave at the thought of being considered part of the UK!)
Bombay isn't as grand and wide and sweeping as Delhi, with its huge gardens and public spaces. It's a busy, crowded, smelly, hurried commercial hub. Space is at a premium here. But yes, there are plenty of parks here. Many of them are open to the public, and run by the city.
Since it is a congested city, where the average citizen does not have his own patch of green, people flock there of an evening to walk, play, exercise, sit around, romance, eat peanuts - and do dope, aside from other vices.
The other alternative is the nearest stretch of sea-front. No board-walks and the like, but the air is clean and the breeze is refreshing. But for most, getting to a sea-front would be a bit of an excursion, since this is such a vast city, so the local park it is.
No fishponds or aviaries that I know of though.
Bangalore, in the South of India, is called The Garden City. Being about 900 metres above sea level (if I remember my school geography right), it's much cooler than other southern cities. Winter temperatures can go to around 12C, and it also gets a lot of rain through the year, so it's very, very green, and filled with parks of all sizes and descriptions, up to the huge Cubbon Park, which has long beautiful walks, a bandstand, and lots and lots of huge trees.